Ministers have vastly underestimated the cost of implementing David Cameron's "bonfire of the quangos", according to a report by Whitehall's spending watchdog.

The National Audit Office (NAO) said the transition costs would be at least £830m – almost double the £425m it says ministers estimated when they launched the plan in October 2010.

The government has previously claimed it would save the taxpayer £2.6bn by 2014/15 by axing 262 public bodies by various means in the biggest Whitehall restructuring for decades.

The result of the extra costs, according to the report, is that the government will now have to find total savings of £3.5bn if they are to meet the 2014/15 target.

The NAO said there was still "insufficient grasp" in departments of the continuing costs of the functions that were being transferred from bodies that had been abolished to other parts of government.

Savings would have to be found elsewhere in Whitehall in order to meet the costs of these newly acquired functions, the report said. The NAO also questioned whether it would improve accountability, as the government claimed. Of the £64bn spent on public bodies in the programme, more than £43bn was still going to arm's-length organisations not directly answerable to ministers.

A third of all money spent by bodies in the public bodies reform programme (£20.6bn) will be subject to greater accountability to elected politicians, but most (£43.2bn) will remain at arm's-length. Despite greater accountability being the programme's primary intended benefit, only one of the six departments examined by the office had proposals for a well-defined measure of success.

Amyas Morse, the head of the NAO, said that the government was not doing enough to secure value for money. "I would expect departments to have a better grasp of the costs of reorganising bodies and of carrying on functions that have been transferred."

A Cabinet Office spokesman said: "Reform of the quango state has been a huge task and when our reforms are complete we will have reduced the number of public bodies by almost a third.

"As we have always acknowledged, there will be one-off costs of the transition, which will be around £600m to £900m.

"Our savings are net of these costs and will continue into the future as a lasting legacy to the taxpayer."

In a separate report on Friday, a powerful parliamentary committee warns that the new arrangement of splitting the job of cabinet secretary and head of the civil service could lead to weak leadership and disperse power. The public administration committee has said that the new roles, occupied by Sir Jeremy Heywood and Sir Bob Kerslake respectively, will not succeed unless ministers, and particularly the prime minister, accords the two roles equal power and status.

The report includes evidence from all four former surviving cabinet secretaries expressing deep reservations about splitting the role of the cabinet secretary. "The risk is that the cabinet secretary will be 'top dog', and the head of the civil service will be relegated to a subservient role rendering him ineffective," the report states.

Bernard Jenkin MP, chair of the committee, said civil servants should not be "mere servants" of ministers: "There must be no impression that the most senior civil servants are becoming political courtiers. They play a vital role in our national life. Nor is this the time to divide or dilute civil service leadership. The head of the civil service cannot be reduced to cutting ribbons at job centres on Friday afternoons," he said.